Question 393: Current Electricity

Question

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P
1
, P
2
and P
3
respectively, then :
![](https://imagex.cdn.examgoal.net/46E1VODPmXCNsQCct/MNqnKAj6kbKjqCXivyfLo0Pfb4iYD/8SGbjXzv25dOPz0YD13QSF/image.png)

Accepted Answer

We have the following cases :
$\bullet$ For configuration (I) : Considering as Wheatstone's bridge, we get the equivalent resistance as ${({R_I})_{eq}} = 1\,\Omega $.
$\bullet$ For configuration (II) : The given configuration is further reduced as follows:
That is, ${({R_{II}})_{eq}} = {1 \over 2}\,\Omega $.
$\bullet$ For configuration (III) : Similarly, we get ${({R_{III}})_{eq}} = 2\,\Omega $.
The power is given by
$P = {{{V^2}} \over R}$
Since V is the same for all three configurations, we have the power as a quantity indirectly proportional to the resistance :
$P \propto {1 \over R}$
From the above three case, we have ${({R_I})_{eq}} = 1\,\Omega ;\,{({R_{II}})_{eq}} = {1 \over 2}\,\Omega ;\,{({R_{III}})_{eq}} = 2\,\Omega $, which implies that
${R_{II}} > {R_I} > {R_{III}}$
Therefore, ${P_2} > {P_2} > {P_3}$
![](['https://app-content.cdn.examgoal.net/fly/@width/image/1l36s8aw4/04a3edaf-f0fa-4a16-b0d0-4e8cd9ff2fb4/5e7e8e40-d405-11ec-b808-5752a3163b13/file-1l36s8aw5.png?format=png', 'https://app-content.cdn.examgoal.net/fly/@width/image/1l36s96og/c87da17a-dbe0-4b24-99c8-dd8966edcb73/770cb810-d405-11ec-b808-5752a3163b13/file-1l36s96oh.png?format=png'])

Answer

P
1
>  P
2
>  P
3

Answer

P
1
>  P
3
>  P
2

Answer

P
2
>  P
1
>  P
3

Answer

P
3
>  P
2
>  P
1

Current Electricity

The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P 1 , P 2 and P 3 respectively, then :

Choose the correct answer: